Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]
↓
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{-1 \cdot im} + e^{im}\right)\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)
↓
\left(0.5 \cdot \sin re\right) \cdot \left(e^{-1 \cdot im} + e^{im}\right)
double f(double re, double im) {
        double r21858 = 0.5;
        double r21859 = re;
        double r21860 = sin(r21859);
        double r21861 = r21858 * r21860;
        double r21862 = 0.0;
        double r21863 = im;
        double r21864 = r21862 - r21863;
        double r21865 = exp(r21864);
        double r21866 = exp(r21863);
        double r21867 = r21865 + r21866;
        double r21868 = r21861 * r21867;
        return r21868;
}
↓
double f(double re, double im) {
        double r21869 = 0.5;
        double r21870 = re;
        double r21871 = sin(r21870);
        double r21872 = r21869 * r21871;
        double r21873 = -1.0;
        double r21874 = im;
        double r21875 = r21873 * r21874;
        double r21876 = exp(r21875);
        double r21877 = exp(r21874);
        double r21878 = r21876 + r21877;
        double r21879 = r21872 * r21878;
        return r21879;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0.0 - im} + e^{im}\right)\]

  2. Taylor expanded around inf 0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\left(e^{im} + e^{-im}\right)}\]

  3. Simplified0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \color{blue}{\left(e^{-1 \cdot im} + e^{im}\right)}\]

  4. Final simplification0.0

    \[\leadsto \left(0.5 \cdot \sin re\right) \cdot \left(e^{-1 \cdot im} + e^{im}\right)\]

Reproduce

herbie shell --seed 2020065 
(FPCore (re im)
  :name "math.sin on complex, real part"
  :precision binary64
  (* (* 0.5 (sin re)) (+ (exp (- 0.0 im)) (exp im))))